Reaction times for detecting the onset of targets on attended objects are faster than reaction times for detecting the onset of targets on unattended objects. Such findings suggest that spatial attention selects objects and not just locations. Some theories posit that visual attention acts on perceptual surfaces, such that once attention is drawn to one location on an object's surface it spreads obligatorily to other locations on that surface even when the observer is performing a task unrelated to those other locations. We used steady-state visual evoked potentials (SSVEP) to study object-based attention in the absence of task demands for target detection or action planning with respect to the attended object. Attention has been shown to modulate SSVEPs, and unlike transient flashes used in classical event related potential (ERP) studies, SSVEP procedures do not draw bottom-up attention and can be used to study attention over extended periods of time. Our stimuli consisted of a ‘plus sign’ configuration in which a horizontal bar either partially occluded the vertical bar (in On-object trials) or appeared partially occluded behind it (in Outside-object trials). We presented task-irrelevant, concentric semi-circular flickering stimuli on the two ends of the horizontal bar while subjects fixated the center of the plus sign. We ‘locked’ attention to the central (intersecting) region of the bars by asking observers to spend several seconds counting the randomly-timed occurrences of low contrast ‘target’ flashes in the central region. No target ever appeared on the ends of the bars. SSVEP power was higher in On-object trials compared to Outside-object trials. Consistent with prior findings on attentional modulation of SSVEP, this differential effect was seen only with some frequencies and contrasts of the flicker. Our results show that attention spreads across the entire attended object even when there is no task benefit for doing so.